Control charts are one of the most important tools of statistical process control. Many control charts have been developed for the monitoring of time between events. However, there are situations for which magnitude of events is also important and needs to be monitored along with the time between them. In this case, simultaneous monitoring of both time between and magnitude of events can be very efficient in detecting process changes. Therefore, a single control chart, referred to as the median-rate chart, is developed in this paper for simultaneous monitoring of magnitude and frequency of events. It is supposed that the magnitude and frequency of events are independent, and follow gamma and exponential distributions, respectively. The proposed chart is based on the ratio of magnitude and time between events and the median of these variables. The results of the performance evaluation represent that the median-rate chart mostly outperforms the existing charts in detecting both small and large shifts of the process. We use the average time to signal for comparing the power of the control charts in detecting out-of-control conditions. Finally, some examples are illustrated to show the applicability of the proposed chart.

中文翻译：

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用于同时监测事件频率和幅度的中值速率控制图

控制图是统计过程控制最重要的工具之一。已经开发了许多控制图来监控事件之间的时间。但是，在某些情况下，事件的大小也很重要，需要与它们之间的时间一起监控。在这种情况下，同时监控事件之间的时间和大小可以非常有效地检测过程变化。因此，本文开发了一个单一的控制图，称为中值率图，用于同时监测事件的幅度和频率。假设事件的大小和频率是独立的，分别服从伽马和指数分布。建议的图表基于事件之间的幅度和时间的比率以及这些变量的中位数。绩效评估的结果表明，中值率图表在检测过程的大小变化方面大多优于现有图表。我们使用平均时间来比较控制图在检测失控条件方面的能力。最后，举例说明了所提出图表的适用性。